
theorem
for L being add-associative right_zeroed right_complementable
            non empty addLoopStr
for S being Subset of L
for a being Element of L holds a in S iff -a in -S
proof
let L be add-associative right_zeroed right_complementable
         non empty addLoopStr;
let S be Subset of L, a be Element of L;
now assume -a in -S;
  then -- a in --S;
  hence a in S;
  end;
hence thesis;
end;
